Answer:
22
Step-by-step explanation:
Which of the following statements are true about the function y = 3x?
1 answer:
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Answer:
Car A ⇔ 50 mph
Car B ⇔ 60 mph
Car C ⇔ 55 mph
Step-by-step explanation:
The equation of the proportionality is y = m x, where m is the constant of proportionality we can find it by using the initial values os x and y or by the rule of the slope of a line m =
Let us find the constant of proportionality of each car
Car A
∵ The line in the figure passes through points (0, 0) and (1, 50)
∴ x1 = 0 and y1 = 0
∴ x2 = 1, y2 = 50
→ By using the rule of the slope above
∵ m = =
∴ m = 50
∴ The constant of proportionality of car A is 50 mph
Car B
∵ The equation of proportionality is y = m x
∵ From the given table at x = 1, y = 60
→ Substitute them in the equation to find m
∴ 60 = m (1)
∴ 60 = m
∴ m = 60
∴ The constant of proportionality of car B is 60 mph
Car C
∵ The equation is y = 55x
→ Compare it with the form of the equation of the proportionality
∵ y = m x
∴ m = 55
∴ The constant of proportionality of car C is 55 mph
In general, you solve a problem like this by identifying the vertices of the feasible region. Graphing is often a good way to do it, or you can solve the equations pairwise to identify the x- and y-values that are at the limits of the region.
In the attached graph, the solution spaces of the last two constraints are shown in red and blue, and their overlap is shown in purple. Hence the vertices of the feasible region are the vertices of the purple area: (0, 0), (0, 1), (1.5, 1.5), and (3, 0).
The signs of the variables in the contraint function (+ for x, - for y) tell you that to maximize C, you want to make y as small as possible, while making x as large as possible at the same time. The solution space vertex that does that is (3, 0).
